batmanmg wrote:the only reason we can't point to the fourth dimension is that our bodies cannot produce a force in the fourth dimension becuase no part of our body exists in the fourth dimension... action requires equal and opposite action... we have nothing to push off of to get ourhand in those directions otherwise it would be a peice of cake and i could raid several banks right now.

Really?

So tell me, what is the function of the 4th dimension then? If we cannot produce forces into the 4th dimension, then the 4th dimension cannot produce forces back onto us. Known as Newtons Third Law, which you somewhat stated.

Thus, if we are uneffected by 4D forces, then what is the function of the 4th dimension?

All this debate on whether you can imagine it or not, and it might not even exist! It certainly DOES NOT exist if it has no function within the Universe.

batmanmg wrote:is it actualy possible to fully visualize a tesseract? Like actualy have a complete image of one in your mind?

Maybe, maybe not. But I have a fairly good grasp of visualizing 4D polytopes in my mind's eye. In fact, I've independently (re-)discovered several 4D Archimedean polytopes simply by visualizing how their cells connect, and verified my conclusions with George Olshevsky's polytopes page. (I even correctly counted the numbers of each type of cell, although this part is a bit questionable since I did rely a bit on second-hand knowledge such as the number and orientation of simpler polytopes.)

I also managed to visualize the duocylinder before I realized it was the duocylinder. I had already read about the duocylinder, but had no idea what it might look like, and at the same time I had managed to visualize this strange torus-like cylindrical object that I didn't know the name of. Then I learned that the two were actually the same object.

Funnily enough, even though I can visualize 4D polytopes with relative ease, I have a lot of trouble visualizing 2D planes embedded in 4D. Especially ones that are twisted in both dimensions at a time, such as the Klein bottle or the knotted 2-sphere.

batmanmg wrote:the only reason we can't point to the fourth dimension is that our bodies cannot produce a force in the fourth dimension becuase no part of our body exists in the fourth dimension...

also becuase you cant face in that direction so the photons cant hit your eyes.

Now, this is actually a very interesting area of speculation...

Imagine a 2D being, say in a roughly hexagonal shape, moving around on the plane. Suppose that this plane actually resides on a table of a 3D being, although the hexagon has no way of directly knowing this. Now, light in the 3D room actually would reach the hexagon: in fact, at every point of its body, both inside and outside. Of course, it doesn't know the real nature of this "background radiation", which appears simply as an inherent property of 2D space.

Now, suppose that one day this 2D being somehow guesses at what is really going on. How would it detect 3D light? It could build a 2D array of cells that are stimulated by this external source, and wire them in such a way that a 3D image could be captured (i.e., 2D projections of objects in 3D space). From the hexagon's point of view, the array of cells cannot possibly capture any image, at least, not any light within the 2D world itself. The only way light can reach cells surrounded by other cells is if it came from outside the 2D plane.

So, in a way, if a 4D world really exists out there, and if our 3D space were actually an open surface in 4D space, then theoretically it is possible to build a 3D block of detectors, which, if they can somehow be made sensitive to 4D light, could capture 4D images (i.e., 3D projections of objects in 4D space). Of course, we would have no way to directly manipulate any 4D objects seen in this way, and only a very limited way of orienting the "camera", so this would be a completely passive vision. But still, it is certainly possible, at least in theory.

Of course, all bets are off as to whether our 3D space is really an open space lying on a 4D surface somewhere... it may be that, if 4D space exists at all, we may simply be "sandwiched" between two solid 4D layers (which explains why we only ever perceive 3 macroscopic dimensions), and thus have no way to look very far into 4D space (and there is nothing interesting to look at either, just a blank wall on either side that we can't see through).

Of course, it doesn't know the real nature of this "background radiation", which appears simply as an inherent property of 2D space.

Interesting that you call it that. Is it possible that the background radiation we see is not evidence of the big bang at all, but evidence of a 4th dimension? It would have to work so that light can enter our realm, but not escape from it. Otherwise all forces would follow an inverse cube law.

I wonder, if Fred saw light from the 3D room, would it appear to be going slower, because it's coming in at an angle that shouldn't exist?

So, in a way, if a 4D world really exists out there, and if our 3D space were actually an open surface in 4D space, then theoretically it is possible to build a 3D block of detectors, which, if they can somehow be made sensitive to 4D light, could capture 4D images (i.e., 3D projections of objects in 4D space).

The temperature of any object would be higher than it should be, and it would gradually increase, unless Fred can radiate the heat back out into 4D. I'm sure there would still be a noticable effect, at least if something changed out there.

Of course, it doesn't know the real nature of this "background radiation", which appears simply as an inherent property of 2D space.

Interesting that you call it that. Is it possible that the background radiation we see is not evidence of the big bang at all, but evidence of a 4th dimension? It would have to work so that light can enter our realm, but not escape from it. Otherwise all forces would follow an inverse cube law.

Well, I'm making no assumptions about whether 4D light is the same as 3D light. It could well be that 4D photons are a different particle entirely from the 3D photons we know and love. Also, if 4D photons have the full 4 degrees of freedom, then there is no reason they should be confined to the 3D hyperplane once they strike it. They would strike 3D atoms in a direction perpendicular to 3-space, of course, which may show up as other side-effects.

I wonder, if Fred saw light from the 3D room, would it appear to be going slower, because it's coming in at an angle that shouldn't exist?

Probably not, because the 4D light would only be visible at, say, W=0, and in the next instant, it would have passed the 3D hyperplane and be no longer detectable.

So, in a way, if a 4D world really exists out there, and if our 3D space were actually an open surface in 4D space, then theoretically it is possible to build a 3D block of detectors, which, if they can somehow be made sensitive to 4D light, could capture 4D images (i.e., 3D projections of objects in 4D space).

The temperature of any object would be higher than it should be, and it would gradually increase, unless Fred can radiate the heat back out into 4D. I'm sure there would still be a noticable effect, at least if something changed out there.

If 4D light has a path to reach the 3D world, then it must necessarily have a path to leave by reflecting off the 3D hyperplane.

I'm not sure about how exactly 4D particles (or whatever it is that comprise 4D objects, if indeed they are out there) would interact with 3D particles.

Perhaps the particles in our world are really prismatic 4D particles trapped for whatever reason on a 3D surface, and so their interactions are largely restricted to 3-space, but they actually have 4D thickness to them. If you like, you could think of matter waves in our 3D world as ripples on the 3D surface of a 4D ocean. (OK, I know matter waves don't quite generalize like that, but it's an interesting thought. Maybe the reason we have no idea what is 'waving' in a matter wave is because it's waving in a 4th direction?) If anything splashed in this ocean, we'd see it as an outburst of energy emanating from a point somewhere in space... quasars, perhaps? Or supernovae.

Probably not, because the 4D light would only be visible at, say, W=0, and in the next instant, it would have passed the 3D hyperplane and be no longer detectable.

I'm assuming that most of the photons simply pass through our hyperplane, but a few of them get absorbed by atoms in the detector.

If 4D light has a path to reach the 3D world, then it must necessarily have a path to leave by reflecting off the 3D hyperplane.

Who says the hyperplane is reflective? Most particles pass through it, but some get absorbed by atoms. It's possible that atoms only radiate back into our realm. Except that might violate conservation of momentum.

Perhaps the particles in our world are really prismatic 4D particles trapped for whatever reason on a 3D surface, and so their interactions are largely restricted to 3-space, but they actually have 4D thickness to them. If you like, you could think of matter waves in our 3D world as ripples on the 3D surface of a 4D ocean. (OK, I know matter waves don't quite generalize like that, but it's an interesting thought. Maybe the reason we have no idea what is 'waving' in a matter wave is because it's waving in a 4th direction?) If anything splashed in this ocean, we'd see it as an outburst of energy emanating from a point somewhere in space... quasars, perhaps? Or supernovae.

Possible, except quasars and supernovae already have a pretty good explanation. A splash like that would appear to violate conservation of energy or mass (it wouldn't really, but it would look like that to us).

Probably not, because the 4D light would only be visible at, say, W=0, and in the next instant, it would have passed the 3D hyperplane and be no longer detectable.

I'm assuming that most of the photons simply pass through our hyperplane, but a few of them get absorbed by atoms in the detector.

Right, assuming, of course, that we know exactly how to know when 4D light has struck the atom. Or what atom would react to 4D light in the first place. (Again, not making any assumptions about how 4D light would interact with 3D atoms.)

If 4D light has a path to reach the 3D world, then it must necessarily have a path to leave by reflecting off the 3D hyperplane.

Who says the hyperplane is reflective? Most particles pass through it, but some get absorbed by atoms. It's possible that atoms only radiate back into our realm. Except that might violate conservation of momentum.

Right, and since we don't observe things like this, it must be that either our 3D world is insulated from 4D radiation, perhaps trapped between two 4D blocks (provided, of course, that we're actually embedded in a 4D world), or 4D radiation does not interact with 3D atoms in the same way 3D light does.

Perhaps the particles in our world are really prismatic 4D particles trapped for whatever reason on a 3D surface, and so their interactions are largely restricted to 3-space, but they actually have 4D thickness to them. If you like, you could think of matter waves in our 3D world as ripples on the 3D surface of a 4D ocean. (OK, I know matter waves don't quite generalize like that, but it's an interesting thought. Maybe the reason we have no idea what is 'waving' in a matter wave is because it's waving in a 4th direction?) If anything splashed in this ocean, we'd see it as an outburst of energy emanating from a point somewhere in space... quasars, perhaps? Or supernovae.

Possible, except quasars and supernovae already have a pretty good explanation. A splash like that would appear to violate conservation of energy or mass (it wouldn't really, but it would look like that to us).

Which, again, shows that if indeed we're embedded in a 4D world, 4D matter doesn't interact with 3D matter the same way as other 3D matter.

4D matter doesn't interact with 3D matter the same way as other 3D matter.

There's a lot of different ways 3D matter can interact with itself. Particles can be absorbed and add energy, collide and bounce away, combine into a new particle, break particles apart, decay, or just pass through. How would a 4D particle interact if not one of these interactions?

4D matter doesn't interact with 3D matter the same way as other 3D matter.

There's a lot of different ways 3D matter can interact with itself. Particles can be absorbed and add energy, collide and bounce away, combine into a new particle, break particles apart, decay, or just pass through. How would a 4D particle interact if not one of these interactions?

No idea. So maybe we aren't connected to a 4D world after all.

Either that, or 4D matter is so different from 3D matter that we don't observe any obvious effects unless we setup something to specifically detect it. Maybe just as light bouncing off the desk is more or less even, it would require not just an array of receptors, but a way to focus light like the lens or pinhole does for a camera. Otherwise you just get white noise, which provides no information. I'm thinking that perhaps vacuum energy is just ambient lightning in 4D, and we have no way of reaching into 4D to build something that can focus the light enough to image it.

But this is all pure speculation anyway. I doubt that a 4D world, if indeed one exists, would be connected with the 3D world in such an obvious way, since otherwise we'd have known about it for sure. As someone once pointed out, if 3D space is embedded in 4D space, why haven't we discovered the membrane of a 2D universe somewhere in 3D space? The fact that there are so many conservation laws in physics seems to indicate that our 3D universe is probably completely self-contained. Any interaction with other spaces seems to be confined to less observable phenomena.

I think it's a lot more fruitful to explore the possibilities of 4D space in and of itself than to try to link it to the real universe.

Either that, or 4D matter is so different from 3D matter that we don't observe any obvious effects unless we setup something to specifically detect it.

It doesn't have to be different, it just has to be difficult to detect. Just like neutrinos or gravitons. Or we already know it's there, but we don't know that it's from the fourth dimension. Like background radiation, or dark matter/energy.

Either that, or 4D matter is so different from 3D matter that we don't observe any obvious effects unless we setup something to specifically detect it.

It doesn't have to be different, it just has to be difficult to detect. Just like neutrinos or gravitons. Or we already know it's there, but we don't know that it's from the fourth dimension. Like background radiation, or dark matter/energy.

Well obviously you can imagine it , but its impossible to have a 2D thing in our dimension, because our dimension has 3 dimensions, and cant harbor something with two. if you want to imagine a 2D line, in your head that is, just imagine a line, but make no height or breadth in it. like a stick figure, but a real one, that cant go left/right

"Civilization is a race between education and catastrophe."-H.G. Wells

XVX wrote:You will never imagine two identical boxes, one inside the other, with their vertices connected by right angles.

I agree that is not consistent in the context of euclidean geometry. Though perhaps with a loose enough sense of "imagine" one might, like the Red Queen, imagine six impossible things before breakfast. One inside the other? Not with all 90 degree angles between the edges. Not possible in this context.

However, I can readily imagine something different: two identical boxes (by which I assume you mean cubes), each existing in a space parallel to the other -- and with their corresponding vertices connected orthogonally.

I can't even visualize a cube without seeing it as a 2-D projection. However, my imagination is not limited to visualization. I imagine 3-D and 4-D objects as if I "feel" their spatial extension, rather than see it. To me, visualization implies sight, and my sight is strictly 2-D.

I can't even visualize a cube without seeing it as a 2-D projection. However, my imagination is not limited to visualization.

-zeroIts very easy to visualize (in your mind) a cube without a 2D projection. Just either use your common sense o_0 or imagine a square. you can see that with your eyes. then, get 5 more square and put them in your mind, a total of 6. then put the edges together with another square, but in a perpendicular direction. and enclose an area of space inside.. that sounds weird.. just use your common sense..

I imagine 3-D and 4-D objects as if I "feel" their spatial extension, rather than see it. To me, visualization implies sight, and my sight is strictly 2-D.

Whether it works that way for anyone else, I cannot say.

-zero
Yes it works that way for other people too. no one in the 3D can see 3D, they just see the 2D sides of whatever the 3D object is. Although they can use their sense of feel to feel that the cube or whatever is a 3D object, and not 2D. or you can use their mind to preceive the sides that you cant see.

[edit] first quote part written wrong.

"Civilization is a race between education and catastrophe."-H.G. Wells

papernuke wrote:Its very easy to visualize (in your mind) a cube without a 2D projection. Just either use your common sense o_0 or imagine a square. you can see that with your eyes. then, get 5 more square and put them in your mind, a total of 6. then put the edges together with another square, but in a perpendicular direction. and enclose an area of space inside.. that sounds weird.. just use your common sense..

But how would you make the squares not appear skewed? I must escape from this plane!

As I may have mentioned elsewhere, for me all visualization is two-dimensional by definition, because that is what describes my field of vision. I can imagine higher dimensions in other ways, but do not refer to this as visualization (for that reason). That may not correspond with how others use the terminology, so it's probably not a good idea to draw overly broad conclusions from my comments. They apply subjectively.

Can you still visual the relationship of any two pixels? This is significantly harder, but not really hard. To test yourself, can you remove all of the interior pixels? Here's the 3-d version with the interior pixels marked:

Note: I'm not saying this a way to completely visualize the tesseract. But, it's an easy place to start. Though, I'd also argue, if you can extend this idea to the continuous case, then I think you've achieved visualizing the tesseract.... for what more could one really want out of a visualization than to be able to see all of the relations of each part to each other part?

Thank you. Let me clarify that my answer was semantic. I use the word "visualization" for denote two dimensional representations (because that's how vision works). Of course i understand that one may use the term metaphorically -- visualizing completely abstract ideas, for instance, that no one can possibly see in a literal sense ("visualize world peace," for instance).

I have no trouble conceptualizing higher dimensions in my imagination, and can even get a feel for them in a kinesthetic sense -- just not a strictly visual sense without distortion due to its projection onto 2-D.